[Download PDF] TS ICET 24th May 2019 Shift-1 Paper with Solutions

Instructions

For the following questions answer them individually

Question 71

A train leaves Hyderabad at 6:10 a.m. and reaches Warangal at 9:25 a.m. The average speed of the train is 44 Kmph. Then the distance from Hyderabad to Warangal in km is:

Video Solution

Question 72

A, F are in different rows and columns. B is opposite to F and H is opposite to D, who is in the same rowas that of A, E and G are neighbors
of F. If the personsitting in the rows faces each other and C is immediate right to D, then who1s diagonally nearest to D?

Video Solution

Question 73

If $$+$$ means $$\div$$, $$-$$ means $$\times$$, $$\div$$ means $$+$$ and $$\times$$ means $$-$$. Then the value of $$16 + 4 \div 5 - 3 \times 1$$ is

Video Solution

Question 74

$$a * b = \frac{a^2 + b^2}{ab}, a > 0, b > 0 \Rightarrow \frac{(1 * 2) * (1 * 1)}{1 * 3} =$$

Video Solution

Question 75

If the symbols , #, @, £ represent addition, subtraction, multiplication and division respectively then:
$$\frac{(15 x) @ (12 \# 8) £ (15 \# 2)}{(15 \# 3) @ (12 * 8) £ (5 * 5)} =$$

Video Solution

Question 76

$$\frac{\left(x + \frac{1}{y}\right)^a . \left(x - \frac{1}{y}\right)^b}{\left(y + \frac{1}{x}\right)^a . \left(y - \frac{1}{x}\right)^b} =$$

Video Solution

Solution

$$\left(\frac{x + \frac{1}{y}}{y + \frac{1}{x}}\right)^a\left(\frac{x - \frac{1}{y}}{y - \frac{1}{x}}\right)^b$$

$$= \left(\frac{xy + 1}{xy + 1} \times \frac{x}{y}\right)^a \left(\frac{xy - 1}{xy - 1} \times \frac{x}{y}\right)^b$$

$$= \left(\frac{x}{y}\right)^a \left(\frac{x}{y}\right)^b$$

$$= \left(\frac{x}{y}\right)^{a+b}$$

Hence the answer is option A

Question 77

$$3^a = 5^b = 75^c \Rightarrow c(2a + b) =$$

Video Solution

Solution

$$3^a = 5^b = 75^c = k$$

$$3 = k^{\frac{1}{a}}, 5 = k^{\frac{1}{b}}, 75 = k^{\frac{1}{c}}$$

$$75 = 3 \times 5^2$$

$$k^{\frac{1}{c}} = k^{\frac{1}{a}} \times k^{\frac{2}{b}}$$

$$\frac{1}{c} = \frac{1}{a} + \frac{2}{b}$$

$$c = \frac{ab}{2a + b}$$

$$c(2a + b) = ab$$

Hence the answer is option B

Question 78

$$ab : bc : ca = 3 : 1 : 2 \Rightarrow \frac{a}{bc} : \frac{b}{ca} =$$

Video Solution

Solution

Shortcut

$$ab : bc : ca = 3 : 1 : 2$$

c = 2 a = 6 b = 3

$$\frac{a}{bc} : \frac{b}{ca}$$

$$\Rightarrow \frac{6}{6} : \frac{3}{12}$$

$$1 : \frac{1}{4}$$

$$\Rightarrow 4 : 1$$

Explanation:

$$ab : bc :ca = 3 : 1 : 2$$

$$\Rightarrow \frac{1}{c} : \frac{1}{a} : \frac{1}{b} = 3 : 1 : 2$$

$$c = \frac{k}{3}, a = k, b = \frac{k}{2}$$

Ratio $$c = 2k, a = 6k, b = 3k$$

$$\frac{a}{bc} : \frac{b}{ca}$$

$$\frac{6}{6} : \frac{3}{12}$$

4 : 1

Hence the answer is option B

Question 79

$$a : b = 3 : 5 :: ab = 2535 \Rightarrow a + b =$$

Video Solution

Solution

a = 3k

b = 5k

$$15k^2 = 2535$$

$$k^2 = 169$$

$$k = 13$$

sum $$\Rightarrow 8k = 104$$

Hence the answer is option A

Question 80

$$x = 5 + \sqrt[3]{5} + \sqrt[3]{25} \Rightarrow x^3 - 15x^2 + 60x + 10 =$$

Video Solution

Solution

$$(x - 5)^3 = 5 + 25 + 3 \times 5 (x - 5)$$

$$(x - 5)^3 = 30 + 15 (x - 5)$$

$$(x - 5)[x^2 + 25 - 10x - 15] = 30$$

$$(x - 5)[x^2 - 10x + 10] = 30$$

$$x^3 - 15x^2 + 60x - 50 = 30$$

$$x^3 - 15x^2 + 60x = 30 + 15$$

$$x^3 - 15x^2 + 60x + 10 = 90$$

Hence the answer is option C

CAT Content

TS ICET 24th May 2019 Shift-1

A train leaves Hyderabad at 6:10 a.m. and reaches Warangal at 9:25 a.m. The average speed of the train is 44 Kmph. Then the distance from Hyderabad to Warangal in km is:

A, F are in different rows and columns. B is opposite to F and H is opposite to D, who is in the same rowas that of A, E and G are neighborsof F. If the personsitting in the rows faces each other and C is immediate right to D, then who1s diagonally nearest to D?

If $$+$$ means $$\div$$, $$-$$ means $$\times$$, $$\div$$ means $$+$$ and $$\times$$ means $$-$$. Then the value of $$16 + 4 \div 5 - 3 \times 1$$ is

$$a * b = \frac{a^2 + b^2}{ab}, a > 0, b > 0 \Rightarrow \frac{(1 * 2) * (1 * 1)}{1 * 3} =$$

If the symbols *, #, @, £ represent addition, subtraction, multiplication and division respectively then:$$\frac{(15 * x) @ (12 \# 8) £ (15 \# 2)}{(15 \# 3) @ (12 * 8) £ (5 * 5)} =$$

$$\frac{\left(x + \frac{1}{y}\right)^a . \left(x - \frac{1}{y}\right)^b}{\left(y + \frac{1}{x}\right)^a . \left(y - \frac{1}{x}\right)^b} =$$

$$3^a = 5^b = 75^c \Rightarrow c(2a + b) =$$

$$ab : bc : ca = 3 : 1 : 2 \Rightarrow \frac{a}{bc} : \frac{b}{ca} =$$

$$a : b = 3 : 5 :: ab = 2535 \Rightarrow a + b =$$

$$x = 5 + \sqrt[3]{5} + \sqrt[3]{25} \Rightarrow x^3 - 15x^2 + 60x + 10 =$$

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A, F are in different rows and columns. B is opposite to F and H is opposite to D, who is in the same rowas that of A, E and G are neighbors
of F. If the personsitting in the rows faces each other and C is immediate right to D, then who1s diagonally nearest to D?

If the symbols , #, @, £ represent addition, subtraction, multiplication and division respectively then:
$$\frac{(15 x) @ (12 \# 8) £ (15 \# 2)}{(15 \# 3) @ (12 * 8) £ (5 * 5)} =$$